BOUNDARY-ELEMENT APPROACH FOR AN INVERSE SOURCE PROBLEM OF THE POISSON EQUATION WITH A ONE-POINT-MASS-LIKE SOURCE

An inverse source problem of the Poisson equation is discussed with a boundary-element-like method This method is based on a boundary integr al expression of the Poisson equation. With this method, we can elimin ate the harmonic term in the solution of the Poisson equation using th e solution and flux on the boundary and consider only an inverse probl em of the logarithmic potential. A simple model is used for the source term, and an effective numerical algorithm is presented for the deter mination of the source in this model. A precise error bound for the re sult is also given in the case of constant elements on the boundary. T he applicability of our method and error estimates is illustrated by a numerical example.